Comprehensive surveys of the star formation properties of galactic
nuclei have been carried out using emission-line spectroscopy in
the visible
(Stauffer 1982,
Keel 1983,
Kennicutt et al 1989b,
Ho et al 1997a,
b) and mid-IR
photometry
(Rieke & Lebofsky
1978,
Scoville et al 1983,
Devereux et al 1987,
Devereux 1987,
Giuricin et al 1994).
Nuclear emission spectra with
HII region-like line ratios are found in 42% of bright spirals
(BT < 12.5), with the fraction
increasing from 8% in S0 galaxies
(and virtually zero in elliptical galaxies) to 80% in Sc-Im galaxies
(Ho et al 1997a).
These fractions are
lower limits, especially in early-type spirals, because the star formation
often is masked by a LINER or Seyfert nucleus. Similar detection fractions
are found in 10-µm surveys of
optically selected spiral galaxies, but with a stronger weighting toward
early Hubble types. The nuclear SFRs implied by the
H and IR fluxes span a
large range, from a lower detection limit of ~ 10-4M
year-1 to well over 100
M
year-1 in the most luminous IR galaxies.

The physical character of the nuclear star-forming regions changes
dramatically over this spectrum of SFRs. The nuclear SFRs in most
galaxies are quite modest, averaging ~ 0.1
M
year-1 (median 0.02
M
year-1)
in the H sample of
Ho et al (1997a)
and ~ 0.2
M
year-1 in the (optically selected) 10-µm samples of
Scoville et al (1983),
Devereux et al (1987).
Given the
different selection criteria and completeness levels in these surveys,
the SFRs are reasonably consistent with each other, and this suggests that
the nuclear star formation at the low end of the SFR spectrum typically
occurs in moderately obscured regions
(AH ~
0-3 mag) that are not physically dissimilar from normal disk HII regions
(Kennicutt et al
1989b,
Ho et al 1997a).

However, the IR observations also reveal a population of more luminous
regions, with LFIR ~ 1010-1013L, and
corresponding SFRs on the order of 1-1000
M
year-1
(Rieke & Low 1972,
Scoville et al 1983,
Joseph & Wright
1985,
Devereux 1987).
Such high SFRs are not seen
in optically selected samples, mainly because the luminous starbursts
are uniquely associated with dense molecular gas disks
(Young & Scoville
1991
and references therein), and for normal gas-to-dust ratios, one expects
visible extinctions of several magnitudes or higher. The remainder of this
section
focuses on these luminous nuclear starbursts because they represent a
star formation regime that is distinct from the more extended star
formation in disks and because these bursts often dominate the total
SFRs in their parent galaxies.

The IRAS all-sky survey provided the first comprehensive picture
of this upper extreme in the SFR spectrum.
Figure 6 shows a comparison of the total 8- to
1000-µm luminosities
(as derived from IRAS) and total molecular gas masses for 87 bright
IR-luminous galaxies, taken from the surveys of
Tinney et al (1990),
Sanders et al (1991).
Tinney et al's sample (open circles) includes
many luminous but otherwise normal star-forming galaxies, while
Sanders et al's brighter sample (solid points) mainly comprises
starburst galaxies and a few AGNs. Strictly speaking, these measurements
cannot
be applied to infer the nuclear SFRs of the galaxies because they are
low-resolution measurements and the samples are heterogeneous. However,
circumnuclear star formation sufficiently dominates the properties of
the luminous IR galaxies (e.g.
Veilleux et al 1995,
Lutz et al 1996)
that Figure 6 (solid points)
provides a representative indication of
the range of SFRs in these IRAS-selected samples.

Figure 6. Relationship between integrated
far-infrared (FIR) luminosity and
molecular gas mass for bright IR galaxies, from
Tinney et al (1990;
open circles) and a more luminous sample by
Sanders et al (1991;
solid points). The solid line shows the
typical L/M ratio for galaxies similar to the Milky
Way. The dashed line shows the approximate limiting luminosity
for a galaxy forming stars with 100% efficiency on a dynamic time
scale, as described in the text.

The most distinctive feature in Figure 6 is the
range of IR luminosities.
The lower range overlaps with the luminosity function of normal galaxies
(the lower limit of 1010L is the
sample definition cutoff), but the population of IR galaxies extends
upward to > 1012.5L. This
would imply SFRs of up to
500 M
year-1 (Equation 4) if starbursts are primarily
responsible for the dust heating, about 20 times larger than the highest
SFRs observed in normal galaxies. Figure 6 also
shows that the luminous
IR galaxies are associated with unusually high molecular gas masses,
which partly accounts for the high SFRs. However the typical SFR per unit
gas mass is much higher than in normal disks; the
solid line in Figure 6 shows the
typical L/M ratio for normal galaxies,
and the efficiencies in the IR galaxies are higher by factors of 2-30
(Young et al 1986,
Solomon & Sage
1988,
Sanders et al 1991).
The H2 masses used here have been
derived using a standard Galactic H2 / CO conversion ratio, and
if the actual conversion factor in the IRAS galaxies is lower,
as is suggested by several lines of evidence, the contrast in
star formation efficiencies would be even larger (e.g.
Downes et al 1993,
Aalto et al 1994,
Solomon et al 1997).

The physical conditions in the circumnuclear star-forming disks
are distinct in many respects from the more extended star-forming disks
of spiral galaxies, as is summarized in Table 1.
The circumnuclear
star formation is especially distinctive in terms of the
absolute range in SFRs, the much higher spatial
concentrations of gas and stars, its burst-like nature (in luminous
systems), and its systematic variation with galaxy type.

Table 1. Star formation in disks and nuclei of
galaxies

Property

Spiral disks

Circumnuclear regions

Radius

1-30 kpc

0.2-2 kpc

Star formation rate (SFR)

0-20
M
year-1

0-1000
M
year-1

Bolometric luminosity

106-1011L

106-1013L

Gas mass

108-1011M

106-1011M

Star formation time scale

1-50 Gyr

0.1-1 Gyr

Gas density

1-100
M
pc-2

102-105M
pc-2

Optical depth (0.5 µm)

0-2

1-1000

SFR density

0-0.1
M
year-1 kpc-2

1-1000
M
year-1 kpc-2

Dominant mode

steady state

steady state + burst

Type dependence?

strong

weak/none

Bar dependence?

weak/none

strong

Spiral structure dependence?

weak/none

weak/none

Interactions dependence?

moderate

strong

Cluster dependence?

moderate/weak

?

Redshift dependence?

strong

?

The different range of physical conditions in the nuclear starbursts
is clearly seen in Figure 7, which plots the
average SFR surface densities
and mean molecular surface densities for the circumnuclear disks of
36 IR-selected starbursts
(Kennicutt 1998).
The comparison is identical to the SFR-density plot for spiral disks in
Figure 5,
except that in this case the SFRs are derived from FIR luminosities
(Equation 4), and only molecular gas densities
are plotted. HI observations show that the atomic gas fractions in these
regions are on the order of only a few percent and can be safely
neglected
(Sanders & Mirabel
1996).
The SFRs and
densities have been averaged over the radius of the circumnuclear disk, as
measured from high-resolution CO or IR maps, as described by
Kennicutt (1998).

Figure 7. Correlation between disk-averaged
SFR per unit area and average gas
surface density, for 36 IR-selected circumnuclear starbursts. See
Figure 5 for a similar comparison
for normal spiral disks. The
dashed and dotted lines show lines
of constant star formation conversion efficiency,
with the same notation as in
Figure 5. The error bars
indicate the typical uncertainties for a given galaxy,
including systematic errors.

Figure 7 shows that the surface densities of gas
and star formation in the nuclear starbursts are 1-4 orders of magnitude
higher than in spiral disks overall. Densities of this order can be
found in large
molecular cloud complexes within spiral disks, of course,
but the physical conditions in many
of the nuclear starbursts are extraordinary even by those standards.
For example, the typical mean densities of the largest molecular
cloud complexes in M31, M33, and M51 are in the range of 40-500
M
pc-2, which corresponds to the lower range of
densities in Figure 7
(Kennicutt 1998).
Likewise, the SFR surface
densities in the 30 Doradus giant HII region, the most luminous
complex in the Local Group, reaches 100
M
year-1 kpc-2
only in the central 10-pc core cluster. The corresponding densities
in many of the starbursts exceed these values, over
regions as large as a kiloparsec in radius.

The starbursts follow a relatively well-defined Schmidt law, with
index N ~ 1.4. The
nature of the star formation law is discussed further in
Section 5, where
we examine the SFR vs gas density relation for all of the data taken
together. Figure 7 also
shows that the characteristic star formation efficiencies
and time scales are quite different in the starbursts. The mean conversion
efficiency is 30% per 108 years, six times larger than
in the spiral disks. Likewise, the gas consumption time scale is six
times shorter, about 0.3 Gyr
on average. This is hardly surprising - these objects are
starbursts by definition - but Figure 7
serves to quantify the characteristic time scales for the starbursts.

As pointed out by
Heckman (1994),
Lehnert & Heckman
(1996),
the luminous IR galaxies lie close to the limiting luminosity allowed
by stellar energy generation, for a system that converts all of its
gas to stars over a dynamical time scale. For a galaxy with dimensions
comparable to the Milky Way, the minimum time scale for feeding the
central starburst is ~ 108 years; this is also consistent with
the minimum gas consumption time scale in
Figure 7. At the limit of 100% star formation
efficiency over this time scale, the corresponding SFR is trivially

(5)

The corresponding maximum bolometric luminosity can be estimated using
Equation 4, or by calculating the maximum nuclear energy release
possible from stars over 108 years. The latter is
~ 0.01 c2,
where in this case is the
SFR, and is the
fraction of the total stellar
mass that is burned in 108 years. A reasonable value of
for a
Salpeter IMF is about 0.05; it could be as high as 0.2 if the starburst
IMF is depleted in low-mass stars (e.g.
Rieke et al 1993).
Combining these terms and assuming further
that all of the bolometric luminosity is reradiated by the dust yields

(6)

Using Equation 4 to convert the SFR to FIR luminosity gives
nearly the same coefficient (6 × 1011).
This limiting L/M relation is shown by the dashed line
in Figure 6, and it lies very close to the
actual upper envelope of
the luminous IR galaxies. Given the number of assumptions that
went into Equation 6, this agreement may be partly fortuitous;
other physical processes, such as optical depth
effects in the cloud, may also be important in defining the upper luminosity
limits (e.g.
Downes et al 1993).
However, the main intent of this exercise
is to illustrate that many of the most extreme circumnuclear starbursts
lie near the physical limit for maximum SFRs in galaxies.
Heckman (1994)
extended this argument and derived the
maximum SFR for a purely self-gravitating protogalaxy, and he showed
that the most luminous IR galaxies lie close to this limit
as well. Note that none of these limits apply to AGN-powered galaxies
because the mass consumption requirements for a given mass are
1-2 orders of magnitude lower.

Taken together, these results reveal the extraordinary
character of the most luminous IR starburst galaxies
(Heckman 1994,
Scoville et al 1994,
Sanders & Mirabel
1996). They
represent systems in which a mass of gas comparable to the entire
ISM of a galaxy has been driven into a region on the order of 1 kpc
in size, and this entire ISM is being formed into stars, with almost
100% efficiency, over a time scale on the order of
108 years. Such a catastrophic transfer of mass can
only take place in a violent interaction or merger, or perhaps during
the initial collapse phase of protogalaxies.